Nuprl Lemma : oal_dom_wf2
∀a:LOSet. ∀b:AbDMon. ∀ps:|oal(a;b)|. (dom(ps) ∈ FiniteSet{a})
Proof
Definitions occuring in Statement :
oal_dom: dom(ps),
oalist: oal(a;b),
finite_set: FiniteSet{s},
all: ∀x:A. B[x],
member: t ∈ T,
abdmonoid: AbDMon,
loset: LOSet,
set_car: |p|
Definitions unfolded in proof :
prop: ℙ,
so_apply: x[s],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
dset: DSet,
qoset: QOSet,
poset: POSet{i},
loset: LOSet,
uall: ∀[x:A]. B[x],
finite_set: FiniteSet{s},
member: t ∈ T,
all: ∀x:A. B[x],
dset_of_mon: g↓set,
set_prod: s × t,
dset_list: s List,
pi1: fst(t),
set_car: |p|,
mk_dset: mk_dset(T, eq),
dset_set: dset_set,
oalist: oal(a;b),
oal_dom: dom(ps),
mset_count: x #∈ a,
mk_mset: mk_mset(as),
squash: ↓T,
implies: P ⇒ Q,
sq_stable: SqStable(P),
abdmonoid: AbDMon,
and: P ∧ Q
Lemmas referenced :
sd_ordered_count,
sq_stable__le,
count_wf,
map_wf,
set_prod_wf,
dset_of_mon_wf,
oal_dom_wf,
abdmonoid_abmonoid,
all_wf,
set_car_wf,
le_wf,
mset_count_wf,
oalist_wf,
dset_wf,
abdmonoid_wf,
loset_wf
Rules used in proof :
natural_numberEquality,
because_Cache,
applyEquality,
dependent_functionElimination,
lambdaEquality,
sqequalRule,
hypothesis,
hypothesisEquality,
rename,
setElimination,
thin,
isectElimination,
sqequalHypSubstitution,
lemma_by_obid,
dependent_set_memberEquality,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
imageElimination,
baseClosed,
imageMemberEquality,
introduction,
independent_functionElimination,
productElimination
Latex:
\mforall{}a:LOSet. \mforall{}b:AbDMon. \mforall{}ps:|oal(a;b)|. (dom(ps) \mmember{} FiniteSet\{a\})
Date html generated:
2016_05_16-AM-08_16_33
Last ObjectModification:
2016_01_16-PM-11_58_14
Theory : polynom_2
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